University of Toronto Department of Economics. Nontraded Goods, Market Segmentation, and Exchange Rates

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1 University of Toronto Department of Economics Working Paper 338 Nontraded Goods, Market Segmentation, and Exchange Rates By Michael Dotsey and Margarida Duarte October 01, 2008

2 Nontraded Goods, Market Segmentation, and Exchange Rates Michael Dotsey Federal Reserve Bank Margarida Duarte University of Toronto of Philadelphia July 2008 Abstract Empirical evidence suggests that movements in international relative prices are large and persistent. Nontraded goods, both in the form of final consumption goods and as an input into the production of final tradable goods, are an important aspect driving international relative price movements. In this paper we show that nontraded goods play an important role in the context of an otherwise standard open-economy macromodel. Our quantitative study with nontraded goods generates implications along several dimensions that are more closely in line with the data relative to the model that abstracts from nontraded goods. In addition, contrary to a large literature, standard alternative assumptions about the currency in which firms price their goods are virtually inconsequential for the properties of aggregate variables in our model, other than the terms of trade. Keywords: exchange rates; nontraded goods; distribution services; incomplete asset markets. JEL classification: F3, F41 We wish to thank George Alessandria, Sylvain Leduc, Steve Meyer, Leonard Nakamura, and Diego Restuccia for very useful discussions. We also wish to thank Jacob Goldston and Pauline L. Martin for research assistance. The views expressed in this article are those of the authors and do not necessarily represent those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. address: michael.dotsey@phil.frb.org. Corresponding author. address: margarida.duarte@utoronto.ca. Tel.: Fax:

3 1 Introduction Empirical evidence regarding international relative prices at the consumer level suggests that arbitrage in international markets is not rapid and that these markets are highly segmented. In fact, even markets for tradable goods appear to be highly segmented internationally: in the data, movements of real exchange rates and movements of the relative price of tradable goods across countries are large and persistent. Moreover, the behavior of these relative prices resembles closely the behavior of relative consumer price indices (CPI) across countries for nontraded goods in the short and medium runs. 1 Nontraded goods are an important source of segmentation of consumer markets across countries. In the United States, for instance, consumption of nontraded goods represents about 40 percent of GDP. Distribution services, in turn, represent about 20 percent of GDP. 2 This evidence suggests that final goods contain a substantial nontraded component, which accounts for a large fraction of measured deviations from the law of one price. Moreover, empirical evidence suggests that the degree of tradability of the inputs of a good plays an important role in accounting for its relative price differentials across countries. 3 In this paper we find that nontraded goods play an important role in exchange rate behavior in the context of an otherwise standard open-economy macromodel. Our quantitative study with nontraded goods generates implications along several dimensions that are more closely in line with the data relative to the model that abstracts from nontraded goods. Further, model decompositions of real exchange rate movements into fluctuations in the relative price of tradable goods across countries and fluctuations in the relative price of nontraded goods to tradable goods are broadly consistent with empirical estimates. We build a two-country general equilibrium model of exchange rates that features two roles for nontraded goods: as final consumption and as an input into the production of final tradable goods. Final tradable goods are produced using local and imported intermediate 1 See, for instance, Engel (1999), Obstfeld and Rogoff (2000a), among others. 2 These numbers are computed as the average share of personal consumption of services in private GDP from 1973 to 2004 and the average share of wholesale and retail services and transportation in private GDP from 1987 to The dichotomy between traded and nontraded goods is not, of course, a clear one. Here we adopt a conventional dichotomy that associates services with nontraded goods. 3 See, for instance, the findings in Crucini, Telmer, and Zachariadis (2005). 2

4 traded inputs and nontraded goods. Intermediate traded goods and nontraded goods, in turn, are produced using local labor and capital services. Thus, the model has an inputoutput structure (as in Obstfeld, 2001), where the output of some sectors is used as an input to the production of final goods. In addition to intermediate goods, agents in the two countries also trade one riskless nominal bond. The model is driven by shocks to productivity in the intermediate traded goods sector and the nontraded goods sector. The presence of nontraded goods in the model increases the volatility of exchange rates. Importantly, fluctuations in the relative price of nontraded goods account for a small fraction of real exchange rate volatility, which is broadly consistent with the data. The intuition behind this result hinges on the fact that in the model with nontraded goods, shocks to productivity in the nontraded goods sector generate sharp nominal exchange rate movements. These movements, in turn, generate large fluctuations in the relative price of tradable goods across countries relative to the fluctuations in the relative price of nontraded goods. Also the cross-correlations of exchange rates with other variables are lower in the presence of nontraded goods. These lower correlations hinge on the fact that the benchmark model is driven by two different shocks that, in isolation, have markedly different implications for exchange rate variability and the co-movement of exchange rates with other variables. In contrast to shocks to productivity in the nontraded goods sector, shocks to productivity in the traded goods sector generate a very small response of exchange rates relative to the response of other variables in the presence of nontraded goods. In the absence of nontraded goods, shocks to productivity in the traded goods sector imply larger exchange rate movements and larger co-movements of exchange rates with other variables. Therefore, these different implications of shocks to productivity in the traded and nontraded goods sectors imply that the presence of nontraded goods in the model is associated with more volatile exchange rates and lower cross-correlations of exchange rates with other variables than in the absence of nontraded goods. The discussion of the properties of relative international prices has been closely tied with a discussion on the nature of the pricing decisions by firms. 4 In much of the recent work in open economy models with nominal price rigidities, deviations from the law of one price have 4 See, for instance, Engel (2002), Obstfeld (2001), Obstfeld and Rogoff (2000a), and the references therein. 3

5 been associated with the pricing-setting regime of exporters rather than with the nontraded component of final tradable goods. In particular, deviations from the law of one price are associated with the assumption that consumer markets are segmented and that exporters set prices in the currency of the buyer. In this environment, known as local currency pricing (LCP), an unanticipated nominal depreciation is automatically associated with a deviation of the law of one price for those goods whose prices are not adjusted immediately. Since prices of imported goods respond slowly to exchange rate changes, this pricing mechanism dampens the expenditure-switching effect of nominal exchange rate movements. However, this effect, a central feature of models in which imports are priced in the currency of the seller (producer currency pricing or PCP), is consistent with empirical evidence suggesting that exchange rate movements are positively correlated with a country s terms of trade. 5 Our setup allows us to disentangle the implications of these two alternative pricing mechanisms that are standard in the open-economy macro literature. In our model, different assumptions regarding the pricing decisions of firms are virtually inconsequential for the properties of aggregate variables, other than the terms of trade. In particular, the real exchange rate and the international relative price of final tradable goods behave similarly across the two price setting regimes. This result follows from the fact that trade represents a relatively small fraction of GDP and that the behavior of the nominal exchange rate is close to a random walk. The two pricing assumptions differ with respect to the correlations of the terms of trade and price of imports with other variables in the model. In particular, the terms of trade have a higher positive correlation with exchange rates under producer currency pricing than with local currency pricing. However, it is hard to discriminate between these alternative pricing mechanisms based on these correlations alone. Our paper is related to recent quantitative studies of exchange rate behavior. Corsetti, Dedola, and Leduc (2008a) explore the role of (nontraded) distribution services in explaining the negative correlation between real exchange rates and relative consumption across countries, and Corsetti, Dedola, and Leduc (2008b) examine the behavior of pass-through in a model that includes distribution services. These two papers explore the implications of the lower price elasticity of traded inputs brought about by the location of distribution 5 See Obstfeld and Rogoff (2000b). 4

6 services in the production chain. In contrast, in our framework, the price elasticity of traded inputs is not affected by distribution services. This paper is also related to the work of Chari, Kehoe, and McGrattan (2002), who assume that all goods are traded and explore the interaction between local currency pricing and monetary shocks in explaining real exchange rate behavior. Our study is in the general methodological spirit of theirs, but highlights the importance of nontraded goods in accounting for exchange rate behavior. The paper is organized as follows. In Section 2 we describe the model and in Section 3 we discuss the calibration. Section 4 presents the results and discusses the role of nontraded goods in the model. In Section 5 we consider the implications of alternative price setting mechanisms. In section 6 we discuss the robustness of our results and we conclude in Section 7. 2 The Model The world economy consists of two countries, denominated home and foreign. Each country is populated by a representative household, a continuum of firms, and a monetary authority. A distinctive feature of the model is the input-output structure of the production side of the economy. This structure emphasizes two distinct uses for nontraded goods: as final consumption and as an input into the production of final tradable goods. In what follows, the home country economy is described, starting with production. The consumer s problem is standard and is described later. The foreign country economy is analogous to the home country economy and asterisks denote foreign country variables Production There are three sectors of production in the model: the nontraded goods sector, the intermediate traded goods sector, and the final tradable goods sector. The three sectors are treated symmetrically in assuming that firms in each sector produce a continuum of differentiated 6 As with other open-economy macromodels, there are many variables in our model and notation is complicated. The interested reader can download a table of notation, included as supplementary material on Science Direct along with this article. 5

7 varieties and set prices in a staggered fashion. Figure 1 depicts the production structure of the economy. Capital and labor are employed by firms in the intermediate and nontraded goods sectors to produce a differentiated variety of the intermediate traded good and the nontraded good. With respect to intermediate traded inputs, countries specialize in production. Thus, there are home intermediate goods and foreign intermediate goods. Firms in the final tradable sector combine an aggregate of all varieties of domestic and imported intermediate traded inputs with an aggregate of all nontraded varieties to produce a differentiated variety of a final tradable good. We interpret the nontraded input of final tradable goods as distribution services. 7 The use of nontraded goods in final tradable goods implies that these goods cannot be traded and that consumers cannot arbitrage cross-country price differentials for these goods. Households consume final tradable goods and nontraded goods and invest using final tradable goods. We now describe each sector, first looking at intermediate traded goods, then nontraded goods and, finally, the production of final tradable goods The Intermediate Traded Goods Sector Intermediate traded goods are produced using primary inputs, capital and labor. There is a continuum of firms in this sector, each producing a differentiated variety h, h [0, 1]. The production function is y H,t (h) = z H,t k H,t (h) α l H,t (h) 1 α, where H refers to the home intermediate traded goods sector. The term z H,t represents a productivity shock specific to this sector, and k H,t (h) and l H,t (h) denote the use of capital and labor services by firm h. The real marginal cost of production (common to all firms in this sector) is given by ψ H,t = 1 ( rt ) ( ) α 1 α wt, (1) z H,t α 1 α where r t and w t denote the rental rates of capital and labor. Firms in this sector are monopolistically competitive and each firm sells its variety to firms in the domestic and foreign final tradable goods sectors. Each firm chooses one price, 7 This characterization of nontraded goods used in production is also taken by Burstein, Neves, and Rebelo (2003) and Corsetti, Dedola, and Leduc (2008a). 6

8 denominated in units of domestic currency, for home and foreign markets. 8 Thus, the law of one price holds for intermediate traded inputs. 9 Firms set prices for J periods in a staggered way. That is, each period, 1/J of firms optimally choose prices that are set for J periods. The problem of a firm adjusting its price in period t is described by J 1 max P H,t (0) j=0 [ E t ϑt+j t (P H,t (0) P t+j ψ H,t+j ) y H,t+j (j) ], (2) where y H,t+j (j) = x H,t+j (j) + x H,t+j (j), and x H,t+j(j) and x H,t+j (j) denote the constantelasticity demand curves from home and foreign markets faced by this firm in period t + j. The term ϑ t+j t denotes the pricing kernel, used to value profits at date t+j, which are random as of t, and P t+j is the aggregate price level. In equilibrium, ϑ t+j t is given by the consumer s intertemporal marginal rate of substitution in consumption, β j (u c,t+j /u c,t )P t /P t+j. As is standard in the New Keynesian literature, the price chosen by firms that adjust prices in period t, P H,t (0), is a function of current and future marginal cost, and current and future output. Specifically, P H,t (0) = ς J 1 ς 1 J 1 j=0 E t The Nontraded Goods Sector j=0 Et [βj [ u c,t+j ψ H,t+j y H,t+j ] (j)]. (3) y H,t+j (j) β j u c,t+j P t+j This sector, indexed by N, has a structure analogous to the intermediate traded goods sector. Each firm n, n [0, 1], operates the production function y N,t (n) = z N,t k N,t (n) α l N,t (n) 1 α, where all the variables have analogous interpretations. The price-setting problem for a firm in this sector is J 1 max P N,t (0) j=0 [ E t ϑt+j t (P N,t (0) P t+j ψ N,t+j ) y N,t+j (j) ], 8 Note that, in contrast to Corsetti and Dedola (2005), in our setup the presence of distribution services does not generate an incentive for intermediate traded goods firms to price discriminate across countries. This difference between the two models arises from the different location of distribution services in the production chain. See footnote We note that the alternative pricing assumption under which intermediate goods producers can price discriminate across countries and choose to set prices in the currency of the buyer (local currency pricing) is virtually inconsequential for the properties of aggregate variables in our model, other than the terms of trade. See Dotsey and Duarte (2008). 7

9 where y N,t+j (j) = x N,t+j (j) + c N,t+j (j) represents demand (from the final tradable goods sector and consumers) faced by this firm in period t+j. The real marginal cost of production in this sector is given by ψ N,t = ψ H,t z H,t /z N,t. The optimal price is given by an expression analogous to equation (3) The Final Tradable Goods Sector There is a continuum of firms in this sector, indexed by T, each producing a differentiated variety r, r [0, 1]. Each firm combines all varieties of domestic and imported intermediate traded goods to produce the composite good x T, given by x T,t (r) = [ ] ξ ω 1 ξ H x H,t(r) ξ 1 ξ + (1 ω H ) 1 ξ xf,t (r) ξ 1 ξ 1 ξ, (4) where x H,t (r) and x F,t (r) are Dixit-Stiglitz aggregators of all home and foreign intermediate traded varieties, respectively. That is, for each firm in this sector ( 1 x H = 0 (x H (h)) ς 1 ς ) ς ς 1 dh, (5) where ς is the elasticity of substitution between any two varieties and the r index is suppressed. The foreign intermediate traded good x F is defined in an analogous way. The parameter ξ in equation (4) denotes the elasticity of substitution between home and foreign traded inputs and the weight ω H determines the bias toward the local traded input. Each firm also combines all nontraded varieties to produce x N, using a Dixit-Stiglitz aggregator analogous to (5). Firms then bring the intermediate traded good x T to market by combining it with nontraded goods x N. The production function of variety r of the final tradable good is y T,t (r) = (ω 1 ρ xn,t (r) ρ 1 ρ ) ρ + (1 ω) 1 ρ xt,t (r) ρ 1 ρ 1 ρ, ρ > 0, (6) where ρ denotes the elasticity of substitution between x T,t (r) and x N,t (r) and ω is a weight. The nontraded goods x N used in the production of the final tradable good are interpreted as distribution services and we associate this sector with the wholesale, retail, and trans- 8

10 portation sectors in the data. Since the retail sector, which is composed of firms engaged in the final step in the distribution of merchandise for personal consumption, is the largest of the three sectors that comprise distribution services, we will refer interchangeably to x N,t (r) as distribution or retail services used by firm r and to this sector as the final tradable goods sector or the retail sector. 10 Given prices of each home intermediate traded variety, P H,t (h), h [0, 1], the price index of the home intermediate traded good, P H,t, and the demand functions for each variety, x H,t (h), are obtained by solving a standard expenditure minimization problem subject to (5). 11 In particular, ( 1 P H,t = x H,t (h) = 0 ) 1 (P H,t (h)) 1 ς 1 ς dh, (7) ( ) ς PH,t x H,t. (8) P H,t (h) The price indices of the foreign intermediate traded good and nontraded good, P F,t and P N,t, and the demand for varieties x F,t (f) and x N,t (n), f, n [0, 1], are given by expressions analogous to (7) and (8). Given prices of the domestic and imported intermediate traded inputs, P H,t and P F,t, the price index of the composite intermediate traded input x T,t and demand functions for x H,t 10 In our setup, each firm in the final tradable goods sector combines nontraded inputs x N with a bundle of local and imported traded inputs x T. Alternatively, firms in this sector could incur distribution costs with each intermediate input variety (x H (h) and x F (f), h, f [0, 1]), prior to combining them into a composite traded good, as in Corsetti and Dedola (2005). Note that in this alternative specification, distribution costs lower the price elasticity of intermediate inputs, while in our model they do not. We believe our equations (4) and (6) represent a reasonable specification of the production process for two reasons. First, a large fraction of U.S. trade consists of intermediate inputs that enter into the production of other goods and that do not require a lot of wholesale or retail trade. Second, retail trade is the largest component of distribution services in value added. 11 See, for example, Obstfeld and Rogoff (1996), Chapter 10. 9

11 and x F,t, are obtained as described above. In particular, ( ) 1 P xt,t = ω H P 1 ξ H,t + (1 ω H )P 1 ξ 1 ξ F,t, (9) ( ) ξ PH,t x H,t = ω H x T,t, (10) P xt,t ( ) ξ PF,t x F,t = (1 ω H ) x T,t. (11) P xt,t Given prices P N,t and P xt,t, the real marginal cost of production in the final tradable goods sector, common to all firms in this sector, is ψ T, ψ T,t = [ ω ( PN,t P t ) 1 ρ + (1 ω) ( PxT,t P t ) 1 ρ ] 1 1 ρ. (12) Firms in this sector sell their differentiated varieties to consumers for consumption and investment purposes. These firms set prices for J periods in a staggered way and the problem of a firm adjusting its price in period t is given by J 1 max P T,t (0) j=0 [ E t ϑt+j t (P T,t (0) P t+j ψ T,t+j ) y T,t+j (j) ], where y T,t+j (j) = c T,t+j (j) + i t+j (j) represents the demand (for consumption and investment purposes) faced by this firm in period t + j. The optimal price is given by an expression analogous to equation (3). 2.2 Households The problem of the household is standard. The representative household in the home country maximizes the expected value of lifetime utility, given by U 0 = E 0 t=0 ( β t u c t, l t, M ) t+1, (13) P t where u represents the momentary utility function, l t denotes hours worked, M t+1 /P t denotes real money balances held from period t to period t + 1, and c t denotes consumption of a 10

12 composite good which is an aggregate of the final tradable good c T,t and the nontraded good c N,t, and is given by c t = ( ω 1 γ γ 1 T c γ T,t ) γ + (1 ω T ) 1 γ 1 γ c γ N,t γ 1, γ > 0. (14) The parameter γ denotes the elasticity of substitution between tradable and nontraded goods and ω T is a weight. Given prices of tradable and nontraded goods, P T,t and P N,t, the demand functions for these goods and the consumption-based price index, P t, are obtained as described above and are given by expressions analogous to equations (10), (11), and (9). The consumption of final tradable goods and nontraded goods, c T and c N, are each a Dixit-Stiglitz aggregator as (5) of all the varieties of the tradable and nontraded goods, c T (r) and c N (n), r, n [0, 1], respectively. As before, expenditure minimization problems analogous to the one described above yield demand functions for each individual variety, c T,t (r) and c N,t (n), and the consumption-based prices of one unit of the final tradable good and nontraded good, P T,t and P N,t, given home-currency prices of individual varieties, P T,t (r) and P N,t (n). The representative consumer in the home country owns the capital stock k t, holds domestic currency, and trades a riskless bond denominated in home-currency units with the foreign representative consumer. The stock of bonds held by the household at the beginning of period t is denoted by B t 1. These bonds pay the gross nominal interest rate R t 1. There is a cost of holding bonds given by Φ b (B t 1 /P t ), where Φ b ( ) is a convex function. 12 consumer rents labor services l t and capital services k t to domestic firms at rates w t and r t, respectively, both expressed in units of final goods. Finally, households receive nominal dividends D t from domestic firms and transfers T t from the monetary authority. The period t budget constraint of the representative consumer, expressed in home-currency units, is given by ( ) Bt 1 P t c t + P T,t i t + M t+1 + B t + P t Φ b P t (w t l t + r t k t ) + R t 1 B t 1 + D t + M t + T t. (15) P t The 12 This cost of holding bonds guarantees that the equilibrium dynamics of our model are stationary. See Schmitt-Grohé and Uribe (2003) for a discussion and alternative approaches. 11

13 It is assumed that investment i t is carried out in final tradable goods. This assumption is consistent with empirical evidence suggesting that investment has a substantial nontraded component and that the import content of investment is larger than that of consumption. 13 The law of motion for capital accumulation is ( ) it k t+1 = k t (1 δ) + k t Φ k, (16) k t where δ is the depreciation rate of capital and Φ k ( ) is a convex function representing capital adjustment costs. 14 Households choose sequences of consumption, hours worked, investment, money holdings, debt holdings, and capital stock to maximize the expected discounted lifetime utility (13) subject to the sequence of budget constraints (15) and laws of motion of capital (16). 2.3 The Monetary Authority The monetary authority issues domestic currency. Additions to the money stock are distributed to consumers through lump-sum transfers T t = Mt s Mt 1. s The monetary authority is assumed to follow an interest rate rule similar to those studied in the literature. In particular, the interest rate is given by R t = ρ R R t 1 + (1 ρ R ) [ R + ρr,π (E t π t+1 π) + ρ R,y ln (y t /ȳ) ], (17) where π t denotes CPI-inflation, y t denotes real GDP, and a barred variable represents its target value. 2.4 Market Clearing Conditions and Model Solution The model is closed by imposing standard market clearing conditions for labor, capital, and bonds. We focus on the symmetric and stationary equilibrium of the model. The model is 13 See Burstein, Neves, and Rebelo (2004). 14 Capital adjustment costs are incorporated to reduce the response of investment to country-specific shocks. In their absence the model would imply excessive investment volatility. See, for instance, Baxter and Crucini (1995). 12

14 solved by linearizing the equations characterizing the equilibrium around the steady-state and solving numerically the resulting system of linear difference equations. We now define some variables of interest. The real exchange rate q, defined as the relative price of consumption across countries, is given by q = SP /P, where S denotes the nominal exchange rate (expressed as units of domestic currency per unit of foreign currency). The terms of trade τ represent the relative price of imports in terms of exports in the home country and are given by τ = P F /(SP H ), where P F and SP H are home-currency prices of imports and exports of the home country. Nominal GDP in the home country is given by Y = P c+p T i+nx, where NX = P H x H P F x F represents nominal net exports. Real GDP is obtained by constructing a chain-weighted index as in the National Income and Product Accounts. Finally, note that the crucial condition for real exchange rate determination in models with incomplete asset markets is given by R t = βe t [ uc,t+1 P t+1 P t u c,t ] = βe t [ u c,t+1 S t+1 P t+1 ] S t Pt. u c,t This condition is obtained by combining the first-order conditions for bond holdings by home and foreign households and it equates the intertemporal marginal rate of substitution of domestic money in expectation across countries. The interest rate rule in equation (17) followed by monetary authorities implies that in our model price levels in each country are smooth. Therefore, nominal exchange rates follow real exchange rates closely. 3 Calibration In this section we report the benchmark parameter values used in solving the model. The benchmark calibration assumes that the world economy is symmetric so that the two countries share the same structure and parameter values. The model is calibrated largely using U.S. data as well as productivity data from the OECD STAN database, with a period in our model corresponding to one quarter. The benchmark calibration is summarized in Table 1. 13

15 3.1 Preferences and Production We assume a momentary utility function of the form ( u c, l, M P ) { ( = 1 ( ) η ) 1 σ } M ac η η + (1 a) exp { v(l)(1 σ)} 1. (18) 1 σ P The discount factor β is set to 0.99, implying a 4 percent annual real rate in the stationary economy. The curvature parameter σ is set equal to two. The parameters a and η are obtained from estimating the money demand equation implied by the first-order conditions for bond and money holdings. Using the utility function defined above, this equation can be written as log M t = 1 P t η 1 log a 1 a + log c t + 1 η 1 log R t 1. (19) R t The data consist of M 1, the three-month interest rate on T-bills, consumption of nondurables and services, and the price index is the deflator on personal consumption expenditures. The sample period is 1959:1-2004:3. 15 The estimation yields values of η = 32 and a = Therefore, our calibration is close to imposing separability between consumption and real money balances. Labor disutility is assumed to take the form v(l) = ψ ψ 1 l 1+ψ 1. The parameters ψ 0 and ψ 1 are set to 3.47 and 0.15, respectively, so that the fraction of working time in steady-state is 0.25 and the elasticity of labor supply, with marginal utility of consumption held constant, is 2. This elasticity is consistent with estimates in Mulligan 15 The estimation is carried out in two steps. Because real M1 is nonstationary and not co-integrated with consumption, equation (19) is first differenced. The coefficient estimate on consumption is and is not statistically different from one, so the assumption of a unitary consumption elasticity implied by the utility function is consistent with the data. The coefficient on the interest rate term is 0.021, and we calibrate η to be 32, which implies an interest elasticity of Next, we form a residual u t = log(m t /P t ) log c t log((r t 1)/R t )/(η 1). This residual is a random walk with drift, and we use a Kalman filter to estimate the drift term, which is the constant in equation (19). The estimation procedure neglects sampling error, because in the second stage we are treating η as a parameter rather than as an estimate. 14

16 (1998) and Solon, Barsky, and Parker (1994). The elasticity of substitution between tradable and nontraded goods in consumption, γ, is set to 0.74 following Mendoza s (1995) estimate for a sample of industrialized countries. We assume that the nontraded input and the composite traded input are used in fixed proportions in the production of final tradable goods. 16 Thus the elasticity of substitution ρ is set to There is considerable uncertainty regarding estimates of the elasticity of substitution between domestic and imported goods, ξ. In addition, this parameter has been shown to play a crucial role in key business cycle properties of two-country models. 17 A reference estimate of this elasticity for the United States has been 1.5 from Whalley (1985). Hooper, Johnson, and Marquez (1998) estimate import and export price elasticities for G-7 countries and report elasticities for the United States between 0.3 and 1.5. This elasticity is set to close to the mid-point in this range (0.85). We choose the weights on consumption of tradable goods ω T, on nontraded distribution services ω, and on domestic traded inputs ω H to simultaneously match, given all other parameter choices, the share of consumption of nontraded goods in GDP, the share of distribution services in GDP, and the average share of imports in GDP. 18 Over the period , these shares averaged 0.44, 0.19, and 0.13, respectively, in the United States. For our benchmark model, these shares imply the values ω T = 0.44, ω = 0.38, and ω H = Given these parameter choices, the model implies that the share of nontraded consumption in total consumption in steady-state is This value is consistent with empirical findings for the United States (see, for instance, Stockman and Tesar, 1995). 16 This assumption is standard. See, for instance, Burstein, Neves, and Rebelo (2003), Corsetti and Dedola (2005), and Corsetti, Dedola, and Leduc (2008a and 2008b). The assumption of fixed proportions in retail markets is also common in the industrial organization literature. See, for instance, Tirole (1995). This assumption seems reasonable to us, although overtime the degree of services incorporated in delivering a good to market as well as the distribution of types of retailers offering different amounts of services along with the goods they sell may vary. These features of retailing, however, seem more secular in nature and, thus, the Leontief specification for production in the retail sector appears reasonable for analyzing cyclical behavior. 17 See, for example, Heathcote and Perri (2002), and Corsetti, Dedola, and Leduc (2008a). 18 We measure distribution services in the data as the value added from retail trade, wholesale trade, and transportation excluding transit and ground transportation services. Other expenses that are not included in our measure and that affect the cost of bringing goods to market include information acquisition, marketing, and currency conversion, to name a few. We, therefore, believe our calibration of distribution services leans on the conservative side. We measure consumption of nontraded goods in the data as consumption services. 15

17 The elasticity of substitution between varieties of a given good, ς, is set equal to 10. As usual, this elasticity is related to the markup chosen when firms adjust their prices, which is ς/ (ς 1). This choice for ς implies a markup of 1.11, which is consistent with the empirical work of Basu and Fernald (1997). The benchmark calibration assumes that all firms set prices for four quarters (J = 4). Regarding production, we take the standard value of α = 1/3, implying that one-third of payments to factors of production goes to capital services. 3.2 Monetary Policy Rule The parameters of the nominal interest rate rule (17) are taken from the estimates in Clarida, Galí, and Gertler (1998) for the United States. Specifically, ρ R = 0.9, ρ R,π = 1.8, and ρ R,y = The target values for R, π, and y are their steady-state values, and we assume a steady-state inflation rate of 2 percent per year. 3.3 Capital Adjustment and Bond Holding Costs Capital adjustment costs are modeled as an increasing convex function of the investment to capital stock ratio. Specifically, Φ k (i/k) = φ 0 + φ 1 (i/k) φ 2. This function is parameterized so that Φ k (δ) = δ, Φ k (δ) = 1, and the volatility of HP-filtered consumption relative to that of HP-filtered GDP is approximately 0.64, as in the U.S. data. The bond holdings cost function is Φ b (B t /P t ) = θ b (B t /P t ) 2 /2, as in Neumeyer and Perri (2005). The parameter θ b is set to 0.001, the lowest value that guarantees that the solution of the model is stationary, without affecting the short-run properties of the model. 3.4 Productivity Shocks The technology shocks are assumed to follow independent AR(1) processes z j i,t = Azj i,t 1 +εj i,t, where i = {mf, sv} and j = {U.S., ROW }; mf stands for manufacturing, sv for services, and ROW for rest of world. ε j i represents the innovation to zj i and has standard deviation σ j i. The data are taken from the OECD STAN data set on total factor productivity (TFP) 16

18 for manufacturing and for wholesale and retail services. 19 The data are annual and run from 1971 to 1993, making for a very short sample in which to infer the time series characteristics of these measures. We cannot reject a unit root for any of the series, which is consistent with other data series on productivity in manufacturing, namely that constructed by the Bureau of Labor Statistics or Basu, Fernald, and Kimball (2004). The shortness of the time series on TFP prevents us from estimating any richer characterization of TFP with any precision. 20 The coefficient estimates of the univariate autoregressive processes range from 0.9 for U.S. manufacturing to 1.05 for ROW services. Therefore, we use as a benchmark stationary but highly persistent processes for each of the technology shocks. Based on these simple regressions, we set A = 0.98, and the ratio of the standard deviations of innovations to TFP on manufacturing and services, σ εmf /σ εsv, is set to 2. Then, the level of σ εmf is chosen to match the volatility of GDP. 4 Findings In this section the role of nontraded goods in our model is assessed. We find that the presence of nontraded goods has important implications for the business-cycle properties of the model, bringing it closer to the data along several dimensions. HP-filtered population moments for our model under the benchmark and alternative parameterizations are reported in Table In addition, we report statistics for HP-filtered data, which take the United States as the home country and a composite of its major trading partners as the foreign country for the period 1973:Q1 2004:Q3. 22 Except for net exports, the table reports the standard deviation of variables divided by that of GDP. Net exports is measured as the HP-filtered ratio of net exports to GDP, and the standard deviation reported in the table is the standard deviation of this ratio. Nontraded goods enter the benchmark model in two ways. First, households derive 19 The ROW aggregate comprises Canada, Japan, West Germany, and the United Kingdom. 20 A VAR was estimated to investigate the relationship across the four TFP series. It was hard to make sense of the results. In this regard our results are similar to those of Baxter and Farr (2001), who analyze the relationship between TFP in manufacturing between the United States and Canada. 21 We thank Robert G. King for providing the algorithms that compute population moments. 22 The data are described in the Appendix. 17

19 utility from the consumption of nontraded goods. Second, production of final tradable goods requires a fixed proportion of nontraded inputs and traded inputs. Columns I and II of Table 2 contain statistics for the benchmark economy and for the economy without nontraded goods. 23 The presence of nontraded goods increases the volatility of real and nominal exchange rates relative to GDP. The benchmark model implies that nominal and real exchange rates are about 1.5 times as volatile as real GDP. In our data, dollar nominal and real exchange rates are about 3.3 and 3.2 times as volatile as real GDP. Abstracting from nontraded goods lowers the volatility of the real exchange rate relative to the volatility of real GDP from 1.50 to The effect of nontraded goods on nominal exchange rate volatility is similar. As in the data, exchange rates are highly correlated with each other (0.99) in both versions of the model. There is a large empirical literature that studies real exchange rate fluctuations by decomposing the real exchange rate into the relative price of tradable goods across countries, rer T, and a function of the relative prices of nontraded to tradable goods across countries, rer N. It is important to verify that our model can account for this decomposition. The decomposition is given by log(q) = log(rer T ) + log(rer N ). 24 When using consumer price indices (CPI) to measure the price of tradable goods, empirical evidence suggests that fluctuations in real exchange rates are almost exclusively accounted for by movements in rer CP I T. 25 The corresponding decomposition in our model is log(q) = log(q T ) + log(q N,T ), where q T = SPT /P T, ( ) ω T +(1 ω T )(PN q N,T = /P T) 1 γ 1 1 γ ω T +(1 ω T )(P N /P T ), and 1 γ PT is the consumer price of tradable goods. In our model the variance of q T accounts for 81 percent of the variance of q, which is broadly consistent with the data. 26 That is, even though the presence of nontraded goods increases the 23 Nontraded goods are eliminated by setting the share of distribution services and the share of nontraded consumption goods in GDP to The economy is re-calibrated to match all other targets. 24 See, for example, Engel (1999). 25 Engel (1999), Chari, Kehoe, and McGrattan (2002), and Burstein, Eichenbaum, and Rebelo (2005) find that fluctuations in rert CP I account for more than 95 percent of fluctuations in the U.S. real exchange rate. Also using consumer prices for tradable goods, Betts and Kehoe (2006) find that the trade-weighted average of the contribution of rert CP I for U.S. real exchange rate fluctuations ranges between 81 percent and 93 percent, for different de-trending methods. 26 The variance-decomposition measure used is var(log q T )/(var(log q T ) + var(log q N,T )). This measure allocates the covariance between log q T and log q N,T to fluctuations in log q T in proportion to the relative size of its variance. 18

20 volatility of the real exchange rate, movements in the relative price of nontraded to tradable goods play a small role in real exchange rate movements when using consumer prices. This result follows from the fact that, as we will see later, shocks to productivity in the nontraded goods sector generate sharp nominal exchange rate movements while prices adjust slowly due to the presence of nominal price rigidities. These exchange rate movements, in turn, are associated with movements in the relative price of tradable goods across countries (q T ). The previous decomposition of real exchange rates does not completely isolate the role of fluctuations in the relative price of nontraded goods in accounting for real exchange rate movements since consumer prices include a substantial nontraded component. There is, however, a lack of empirical consensus regarding the importance of fluctuations in the relative price of nontraded goods in real exchange rate volatility. For example, Burstein, Eichenbaum, and Rebelo (2005) use prices at the dock of pure-traded goods to measure rer T. They find that the contribution of movements in the relative price of traded goods in accounting for U.S. real exchange rate fluctuations ranges between 29 and 44 percent. In our model, we can isolate the role of nontraded goods in real exchange rate fluctuations by decomposing q as log(q) = log(q X ) + log(q N,X ), where q X = SPx T /P xt, P xt is the price of the intermediate traded input, and q N,X is a complicated function of P N /P xt and PN /P x T. In our model the variance of q X is found to account for 27 percent of the variance of q. Therefore, our model implies decompositions of real exchange rate variance that are in line with the empirical evidence of Burstein et al (2005). The presence of nontraded goods also brings the cross-correlations of the real exchange rate with other variables closer in line with the data. In particular, the cross-correlations between the real exchange rate and real GDP, the terms of trade, and the ratio of consumption across countries rises as we eliminate nontraded goods. In the benchmark model the crosscorrelations of the terms of trade with nominal and real exchange rates are 0.51 and In the data, the correlations of the U.S. terms of trade with U.S. nominal and real effective exchange rates are 0.39 and In the absence of nontraded goods, the cross-correlation of the terms of trade with exchange rates is To gain some intuition, note that when prices are flexible the real exchange rate can be written as a function of the relative price of nontraded goods across countries, SPN /P N, and 19

21 the terms of trade, τ, using the equations for P, P T, and P xt. In log-linear terms, ˆq t = (1 ω T + ω T ω)(ŝt + ˆP N,t ˆP N,t ) + ω T (1 ω)(2ω H 1)ˆτ t, (20) where a hat represents the deviation from steady-state of the log of the variable. Thus, movements in the real exchange rate are composed of movements in the relative price of nontraded goods across countries weighted by the fraction of consumption composed of nontraded goods, and movements in the terms of trade weighted by the fraction of traded goods (domestic and imported) in consumption. In the absence of nontraded goods, this expression simplifies to ˆq t = (2ω H 1)ˆτ t and it follows that the correlation between these two variables implied by the model is 1. With nontraded goods, the real exchange rate depends both on the terms of trade and the relative price of nontraded goods across countries. As long as these two variables are not perfectly correlated, it follows that the correlation between the terms of trade and the real exchange rate is below one. In our benchmark model with sticky prices, the correlation between the relative price of nontraded goods across countries and the terms of trade is 0.57 and the correlation between the real exchange rate and the terms of trade is In addition to increasing the volatility of exchange rates and providing consistent decompositions of real exchange rate fluctuations, the presence of nontraded goods also lowers the correlation of the real exchange rate with GDP and the ratio of consumption across countries, from 0.64 and 0.99 to 0.47 and The intuition behind these lower correlations hinges on the presence of two exogenous shocks with markedly different implications for exchange rates and other macrovariables. In the absence of nontraded goods, the model is driven by fluctuations in z H only. In this case, shocks to z H generate large movements in exchange rates and other variables. Thus, the correlations between exchange rates and other variables implied by the model are high. In the presence of nontraded goods, however, shocks to z H imply very small responses of exchange rates relative to other variables (and low co-movement between these variables) while shocks to z N imply large responses of exchange rates and high co-movements of exchange rates with other variables. The presence of both shocks in the model with nontraded goods allows exchange rates to exhibit relatively high 20

22 volatility with lower co-movement of exchange rates with other variables. 27 Nevertheless, the model with nontraded goods implies correlations that are large compared to the data. For completeness, other statistics are reported in Table 2. The presence of nontraded goods also brings the cross-country correlations of GDP, consumption, and investment closer in line with the data. With nontraded goods the cross-correlation of consumption falls from 0.54 to 0.40 while the cross-correlation of output increases from 0.16 to Nevertheless, the cross-country correlation of GDP is lower than in the data (0.36 versus 0.57). 28 The model is driven by country-specific shocks to productivity in the traded and nontraded goods sectors. To further understand the role of nontraded goods in our model, we now focus on the role of these goods in the adjustment of the economy following shocks to productivity in each sector. 4.1 Shocks to Traded Goods Productivity The response of selected variables to a positive 1 percent shock to productivity in the traded goods sector is depicted in Figure 2. In response to a positive shock in the home country, the price of home intermediate traded goods falls. Consumption, hours worked, and real GDP fall slightly on impact, but they rise as traded goods firms lower their prices. Since the price of home intermediate inputs falls relative to both foreign intermediate inputs (the inverse of the terms of trade) and nontraded goods, the home country s demand for intermediate inputs increases and home and foreign producers of final tradable goods substitute toward home traded inputs and away from foreign traded inputs. A shock to productivity in the traded goods sector generates a very small response of nominal and real exchange rates. To see why this happens, note first that in this case agents come close to optimally sharing risk to traded goods productivity with one nominal bond only. 29 In addition, note that in the benchmark model home and foreign producers of 27 See Duarte and Stockman (2002) for a related argument. 28 It should be noted that in our benchmark calibration all exogenous shocks are independent across countries, and thus, these positive cross-country correlations reflect the endogenous transmission mechanism of shocks across countries in our model. 29 This feature is standard in two-country models, in which equilibrium allocations with complete asset markets or one riskless bond only are very close. See, for example, Baxter and Crucini (1995), Chari, Kehoe, and McGrattan (2002), and Duarte and Stockman (2005). 21

23 final tradable goods use local and imported goods in roughly the same proportion (ω H = 0.59). That is, the home and foreign economies are close to being symmetric, implying that these shocks do not disproportionately benefit the local economy. Therefore, the effect of a technology shock z H in our setting is very close to what would happen under symmetry and complete asset markets, implying that the real exchange rate does not respond very much to this shock. Since price levels are very smooth, the response of the nominal exchange rate is also small. It also follows that the condition q t = u c,t/u c,t approximately holds in response to these shocks. 30 Combining this condition with the observation that home agents work less relative to foreign agents because prices and demand adjust slowly, implies that, on impact, the foreign agent must consume more relative to the home agent for marginal utilities to be roughly equated (recall that utility is nonseparable). As prices adjust and relative demand for the home intermediate traded good increases, hours worked, and consumption in the home country increase relative to those in the foreign country. Given the small response of exchange rates relative to the response of other variables after a shock to productivity in the traded goods sector, the model would imply low correlations between exchange rates and other aggregate variables if it were driven only by shocks to productivity in the traded goods sector. In this case, the correlations of the real exchange rate with output and the ratio of consumption across countries are 0.36 and In the absence of nontraded goods the model requires a high degree of home bias (as measured by the parameter ω H ) in order for it to match the target import share. In this case ω H = 0.86 and the two countries are no longer close to being symmetric since a positive shock to z H disproportionately benefits local producers of final tradable goods relative to foreign ones. Therefore, in the absence of nontraded goods, this shock is associated with larger exchange rate depreciations and larger responses of other home variables. As a consequence, the co-movement between exchange rates and other variables is larger in the model without nontraded goods (see column II of Table 2). Thus, with respect to a shock to z H, the presence of nontraded goods affects the variability of the exchange rate largely because the degree of home bias must be re-calibrated in order to match the import share. 30 For a derivation of this condition see, for instance, Chari, Kehoe, and McGrattan (2002). 22